1. Random Experiments
Random experiments are fundamental processes in engineering and applied sciences characterized by uncertain outcomes. They form the basis for probability theory, crucial for modeling real-world systems and applications such as heat flow and fluid dynamics. Understanding these experiments leads to a solid grasp of events and their types, operations on events, and their connection to probability, which is vital for solving complex engineering problems.
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What we have learnt
- A random experiment has uncertain outcomes that can be repeated under identical conditions.
- The sample space of an experiment includes all possible outcomes, while events are subsets of this space.
- Different types of events include simple, compound, sure, and impossible events.
Key Concepts
- -- Random Experiment
- A physical situation where the outcome cannot be predicted with certainty, even when the experiment is repeated under identical conditions.
- -- Sample Space
- The set of all possible outcomes of a random experiment.
- -- Event
- A subset of the sample space that includes one or more outcomes.
- -- Union
- An operation that represents either of two events occurring, denoted as A ∪ B.
- -- Intersection
- An operation representing both events occurring, denoted as A ∩ B.
- -- Probability
- A measure of the likelihood of an event, calculated as the number of favorable outcomes divided by the total number of outcomes.
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